A) \[2\sqrt{2}+1\]
B) \[\sqrt{2}-1\]
C) \[\sqrt{2}+1\]
D) \[2\sqrt{2}-1\]
Correct Answer: C
Solution :
\[T:y(\beta )=\frac{1}{2}(x+{{\beta }^{2}})\] \[2y\beta =x+{{\beta }^{2}}\] \[y=\left( \frac{1}{2\beta } \right)x+\frac{\beta }{2}\] \[m=\frac{1}{2\beta };C=\frac{\beta }{2}\] \[\frac{\beta }{2}=\pm \sqrt{\frac{1}{2{{\beta }^{2}}}+\frac{1}{2}}\] \[\frac{{{\beta }^{2}}}{4}=\frac{1}{4{{\beta }^{2}}}+\frac{1}{2}\] \[\frac{{{\beta }^{2}}}{4}=\frac{1+2{{\beta }^{2}}}{4{{\beta }^{2}}}\] \[\Rightarrow \]\[{{\beta }^{4}}-2{{\beta }^{2}}-1=0\] \[{{({{\beta }^{2}}-1)}^{2}}=2\] \[{{\beta }^{2}}-1=\sqrt{2}\] \[{{\beta }^{2}}=\sqrt{2}+1\]You need to login to perform this action.
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